The RKDG(Runge-Kutta Discontinuous Galerkin) finite element method,the Level Set method and the Ghost Fluid method are applied to compressible multimedia fluids.We discretizes Euler equations,the Level Set equation and the reinitialization equation by a DG(Discontinuous Galerkin) method in space and by a Runge-Kutta method in time.Two dimensional compressible two-fluid flows such as air-air,air-liquid are computed.High resolution ratio computational results are obtained.

The RKDG finite element method, Level Set method and modified Ghost Fluid method with Isentropic fix are used to simulate a one-dimensional compressible multicomponent Euler equation. A third-order accurate RKDG finite element method is used to solve the Euler equation, the Level Set equation and the re-initiation equation. Numerical tests on one-dimensional compressible two-fluid flows are made and satisfactory results are obtained.